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Let L denotes the number of values of al...

Let `L` denotes the number of values of `alpha in [0,pi]` which satisfy the equation `cos alpha cos 2 alpha cos 4alpha =1/8`. `M` denotes the smallest positive integral value of `'a'` for which the equation `8x^3 - ax^2 + bx-1=0` has 3 real roots in geometric progression. Find the value of `LM`.

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Let L denotes the number of values of alpha in[0,pi] which satisfy the equation cos alpha cos2 alpha cos4 alpha=(1)/(8).M denotes the smallest positive integral value of ' a' for which the equation 8x^(3)-ax^(2)+bx-1=0 has 3 real roots in geometric progression.Find the value of LM.

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